strange bahavior of ArcSinh

• To: mathgroup at smc.vnet.net
• Subject: [mg110927] strange bahavior of ArcSinh
• From: mathfanda <KKratky at seznam.cz>
• Date: Mon, 12 Jul 2010 01:04:10 -0400 (EDT)

```Dear Mathematica users,

I have found a strange behavior of ArcSinh.
Without ArcSinh this makes a nice graph as expected.
With ArcSinh I get a strange warning in Mathematica 7.0.
Is it a bug or a feature?
Mathematica 5.2 gives no warnings.
Best regards
Pavel

Mathematica 7.0 for Linux x86 (64-bit)

In[1]:= !!test.m
f[b_]:=(
j={{0,1},{-(2b Cos[2t]),0}};
s=NDSolve[{m'[t]==j.m[t],m[0]==IdentityMatrix[2]},m,{t,0,2Pi}]//
First;
Tr[m[2Pi]/.s]
);
p1:=Plot [ f[b],{b,-1,1}];
p2:=Plot [ ArcSinh[f[b]],{b,-1,1}];

In[1]:= <<test.m

In[2]:= p1

Out[2]= -Graphics-

In[3]:= p2

ReplaceAll::reps:
{m'[t] == {{0, 1}, {1.99992 Cos[2 t], 0}} . m[t], m[0] == {{1, 0},
{0, 1}}}
is neither a list of replacement rules nor a valid dispatch
table, and so
cannot be used for replacing.

ReplaceAll::reps:
{m'[t] == {{0., 1.}, {1.99992 Cos[2. t], 0.}} . m[t],
m[0.] == {{1., 0.}, {0., 1.}}} is neither a list of replacement
rules nor
a valid dispatch table, and so cannot be used for replacing.

ReplaceAll::reps:
{m'[t] == {{0, 1}, {1.91829 Cos[2 t], 0}} . m[t], m[0] == {{1, 0},
{0, 1}}}
is neither a list of replacement rules nor a valid dispatch
table, and so
cannot be used for replacing.

General::stop: Further output of ReplaceAll::reps
will be suppressed during this calculation.

Plot::exclul: {Re[Tr[m[2 Pi] /.
{m'[t] == {{0, 1}, {-2 b Cos[2 t], 0}} . m[t],
m[0] == {{1, 0}, {0, 1}}}]] - 0} must be a list of
equalities or
real-valued functions.

Out[3]= -Graphics-

```

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